What your logo lacks is a good concept base, I think by defining this you will achieve a good final result.
At the moment, the only thing regarding concept is strong presence, the rest are purely formal aspects:
- B & W (and shades of gray - not 50 though)
- Minimal almost icon-like
- Sharp (literally, with pointy corners, catholic edges & everything)
- Plus points if the design uses the letters B or Z as it's base
- Further plus points if it is an abstract design (see Sample 3)
- It should not have curves
- It should not have details
With SEVEN formal premises it seems that your client needs a geometrical shape rather than a logo.
I made a Google search using
sharp minimal corners abstract black and white strong icon logo and any of the results fits what your client requires.
So the question is: why does a client look for a graphic designer when putting all the formal words wanted gives a logo result in a simple Google search?
The answer: because he needs something UNIQUE. And where is that uniqueness? This is the essence of a graphic designer, to find a concept that fits some formal requirements and not vice versa, combine some shapes and make them look a company brand (such the process you are doing).
A good exercise is to question these formal precepts:
- It must be Sharp, literally, with pointy corners
Why? Is it related to energy? Is the energy angled? why? by the stereotyped image we have of lightning? Because it's an image that remains in our collective unconscious about electricity? Does the company have anything to do with electricity?
Clients are not graphic designers, usually, and they use to have only ideas about formal aspects, how they want their logo to look. They have the conceptual part too, but they don't know how to express it in words. The job of a good designer involves a lot of psychology, self-questioning about the formal premises the client demands helps to find that concept stuck in their brain. If the designer is able to define each of these formal elements in concepts, the future logo is a guaranteed sale.
As seen in your sketches you are very good at creating and optimizing shapes, knowing you have this capacity, perhaps you should leave the formal part for a while, get a pencil and a paper and develop a good conceptual starting point. I would recommend a minimum of five points, to have five concepts and five formal elements.
This will be a great help, not only to get a very good logo but also to sell it to your client as the unique and relevant logo for their company.
By the way, it would be good to see your question again with the result: five concepts, five formal elements and the logo, but I'm sure you will not need this.